“My advice to [his own self-selected!] trustee could not be more simple: Put 10% of the cash in short-term government bonds and 90% in a very low-cost S&P 500 index fund. (I suggest Vanguard’s.) I believe the trust’s long-term results from this policy will be superior to those attained by most investors — whether pension funds, institutions or individuals — who employ high-fee managers.”

How can Buffett say passive investing is best for most people and also an “enormous advantage” for active investors like him? If it helps everyone else, how can it also help him?

The opposite view is sometimes described as the “suckers at the poker table” hypothesis — the theory that an increase in passive investing is bad for active investors like Buffett because the fewer suckers there are to fleece, the less profit there is for smart active investors.

So which view is right? The “suckers at the poker table” theory, or Warren Buffett, who says passive investors make his job easier? And how can Buffett be right while at the same time saying most people should invest passively?

Let’s do a simple thought experiment: What would happen if everyone was a passive investor except Warren Buffett?

As is often the case, we find that Buffett is way ahead of everyone else. He is both correct and self-serving. Anyone can use an index to match the market on a holding period–return basis, and yet Buffett can still crush everyone else on a money-weighted basis.

A brief theoretical digression: The Grossman-Stiglitz paradox holds that you can’t have a perfectly efficient market because that requires someone to be willing to arbitrage away any inefficient price. But arbitrageurs have to get paid. So they will only step in if they’re compensated for their time, data services, research, compliance, office rent, overhead, and an adequate after-tax, risk-adjusted return.

So markets tend toward an equilibrium where prices are boundedly efficient, where there is no more mispricing than at the level that would make arbitrage profitable.

The set of all investors is the market itself and, in the aggregate in any given period, earns the market return. The subset of index investors, by virtue of owning the market portfolio, also earns the market return. To make the indexers and non-indexers add up to the market, the non-index investors in the aggregate must also earn the market return.1

In the aggregate, those “arbitrageur” active investors aren’t making any excess profits! Before expenses, they are matching the market, and after expenses they are underperforming.

In order to have any profitable active investors, it seems you have to posit overconfident, “dumb” active money that loses money trading against the “smart” arbitrageurs. And that doesn’t make much sense. It implies the persistence of a class of irrational investors. If there’s a tug of war between smart money and dumb money, and a priori the dumb money is as strong as the smart money, and it’s to the smart money’s advantage to trick the dumb money whenever possible, why should that make prices efficient?

It sounds like a theory of irrational traders and not very efficient markets.

Let’s see if another thought experiment can shed some light:

What happens if passive investors take over the market so there is only one active investor left: our hypothetical Warren Buffett?

Let’s disregard for the moment changes in the composition of the index. We only have Buffett trading with passive investors. The passive investors just want to enter and exit the whole market. They don’t want to trade individual stocks or a non-market-weighted portfolio. And there are no other active investors to trade with other than Buffett, who makes a bid-ask market for the index, selling when it’s above his estimate of fair value and buying when it’s below fair value.

A somewhat trivial example, which should be familiar to those who have done the CFA curriculum on holding period vs. money-weighted returns:

Cash Flows

Index
Fair Value

Index
Price

Premium/
Discount

Holding
Period
Return

Cost
Averaging
Investor 1

Dumb
Investor 2

Dumb
Investor 3

Warren
Buffett

Corporate
Issuance

Year 0

$ 100.00

100.00

0%

(1,000)

(1,000)

(1,000)

–

3,000

Year 1

$ 105.00

94.50

-10%

-5.5%

(1,000)

–

945

(1,000)

1,055

Year 2

$ 110.25

121.28

10%

28.3%

(1,000)

(1,000)

(1,000)

1,283

1,717

Final value

$ 115.76

115.76

0%

-4.5%

3,337

2,112

955

–

Holding period return

5.0%

5.0%

5.0%

5.0%

Money weighted return (IRR)

5.4%

2.7%

-5.0%

28.3%

The index fair value grows at 5% per year.

It starts priced at fair value in Year 0, in Year 1 it trades at a 10% discount, in Year 2 at a 10% premium, and then finally returns to fair value in Year 3.

The holding period return, which ignores flows, is 5%, matching the index.

Dollar cost averaging Investor 1 buys $1,000 worth of stock each year and has a money-weighted return of 5.4% as a result of automatically buying more shares when they are cheap and fewer when they are expensive.

Dumb Investor 2 panics when the market goes to a 10% discount and doesn’t buy that year and ends up with a 2.7% money-weighted return.

Dumb Investor 3 panics even worse, sells when the market goes to a 10% discount, and ends up with a -5.0% money-weighted return.

Warren Buffett stays out of the market until it trades at a 10% discount, sells at a 10% premium, and ends up with a 28.3% money-weighted return.

Everyone gets the same 5% holding period return, which ignores flows.

But on a money-weighted, risk-adjusted basis, of course, the returns are very different, and our Warren Buffett crushes the market.

One way of looking at it is Buffett increases the size of the overall pie when the odds are in his favor, shrinks it when they aren’t, and outperforms without necessarily taking anything from the other investors, who earn the market return in each holding period.

Another way of looking at it is to consider the whole scenario as one holding period during which Buffett took advantage of people who were selling low and buying high. Effectively, our Warren Buffett sets a floor under the market when events or cash flows make the passive investor inclined to sell excessively cheap and sets a ceiling when the market gets expensive.

If you examine any individual year, everyone here is a passive investor in the sense of always holding the index. But if you think of the entire scenario as one holding period, only someone who owns the index and never trades is really a passive investor. Everyone else is buying high or selling low within the period.

If you’re planning to invest for an objective other than buying and holding forever, you have to make decisions about when and how much to invest and when and how much to withdraw. On a sufficiently long timeline, the probability of being a completely passive investor goes to zero.

Eventually you have to make an active investment decision, and at that point the shrewd investors are lying in wait. Everyone eventually has to pay Charon to cross the river Styx.

It gets even better for Buffett when you incorporate index changes.

An IPO comes out. The IPO is initially not in the index. Our hypothetical Warren Buffett sets the IPO price. He doesn’t have anyone to bid against or anyone to trade with besides the issuers since the stock is not yet in the index. Being an accommodating fellow, he sets the price at fair value minus his margin of safety, illiquidity discount, etc.

The IPO eventually gets added to the index. Indexers have to buy the stock. Buffett solely determines the price at which it gets added to the index. In his obliging manner, he sets it at fair value for a liquid index stock plus a reasonable convenience premium.

What a sweet deal! Pay a steep discount for any security not in the index and demand a big premium when they go into the index. Similar profits are available when securities exit the index.

Going back to the Grossman-Stiglitz paradox, the arbitrageur active traders can do pretty well, even without the existence of a large pool of permanently underperforming “dumb money,” which is unnecessary and illogical.

They pull a bit of Star Trek’s Kobayashi Maru scenario by going outside the bounds of picking stocks from within the index.

The “suckers at the poker table” paradigm goes astray because there isn’t some exogenous fixed size of the investment pie investors are fighting over. The returns are endogenous: They are in part determined by how smart the investors are, how well the capital in the economy is allocated, and by everything else that impacts economic and market outcomes.

The size of the profits pie is not fixed. When investors take a risk funding an early Apple or Wynn, they increase the size of the overall pie, getting a bigger slice without taking a commensurate amount from everyone else.

Bill Ackman, in his most recent Pershing Square letter, asked “Is There an Index Fund Bubble?” He pointed out that if index funds generally side with management, they make the activist’s job harder. But increased herding can be a self-fulfilling prophecy with bubble dynamics, and it increases opportunities outside liquid indexes.

There are useful parallels between investing and poker, but investing is not a zero-sum game, dumb money is not the primary driver of returns for most strategies, and the “suckers at the poker table” is not a useful analogy for most long-term investors.

1. This accounting excludes issuers of stock, who are kind of important. Companies are net distributors of cash to their stockholders. They pay dividends and they on net buy back stock, these days. So everyone cannot be a passive investor in the S&P and reinvest dividends. If they tried, something would have to give. Investors would bid up stocks until someone capitulated and started selling, or companies started issuing stock, or something. When it’s not a zero-sum game, reasoning from accounting identities tends to be misleading.

All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Druce Vertes, CFA, is the founder of StreetEYE, a social news aggregator for financial market news. Previously, he worked as an analyst, consultant, and IT manager at several major sell-side firms and hedge funds.

14 thoughts on “Active vs. Passive Investing and the “Suckers at the Poker Table” Fallacy”

The spirit of Buffet’s advice is to go passive unless you know what you’re doing. Most would not profess to knowing how to invest but many think they can hire someone who does know. This is a second order game — you need to know how to hire a good professional money manager. Unfortunately even professional investment advisors don’t know good managers from bad, but they could if they’d try harder. See http://www.ppca-inc.com/pdf/Minding-Ps-and-Qs.pdf . investors don’t realize that their advisors are faking their manager selection expertise.

1) The first thought experiment seems to set out to dis/prove the ability of active investors to outperform. It concludes that the existence of active investors will not make market prices more efficient. Those are completely different and independent issues.

I picture my self outperforming at the expense of 25 year old guys who have borrowed money to invest. The possibility for one class of active investors to outperform is not discredited by any conclusion that this will not make the market more efficient. I don’t agree that “dumb money is unnecessary and illogical”.

2) I don’t believe the conclusion of the second thought experiment is determined by some difference in math between money-weighted and holding period returns calculations.

I would present the first issue in the second thought experiment as a dispute of the basic model used by W Sharpe in his famous argument at http://www.stanford.edu/~wfsharpe/art/active/active.htm. He draws circle around just the total of all traded stocks but ignores cash. Almost all investors buy and sell cash along with securities. In my experience trading cash is the easiest and most impact-ful way to beat the market.

3) The other point could be presented as Sharpe’s failure to appreciate that companies go bust, go public, IPO, and pay dividends. In other words profits are made by cash moving between the primary and secondary markets. It is the active investor who will reap profits from trading on the fact that companies’ relative values do NOT stay steady, and eventually the truth will out with either a cash transaction, or cash moving to the secondary market.

These are things that I think are fallacies, that I tried to disprove by a simple example:

1) That the move toward indexing drives dumb money out and makes prices more efficient

2) That everyone can index and get the market return, even after trading costs

To your first point, on the contrary, I believe that active investment makes prices more efficient. There is a Nash-like equilibrium where enough smart people are active investors to make prices boundedly efficient, and adding the marginal active investor doesn’t make prices sufficiently more efficient to offset their expenses.

As more people index, on the one hand they save on expenses, on the other hand liquidity decreases and volatility increases. They pay a higher premium for securities in the index, and a higher toll to get in and out.

Your second point I think is correct, basically it’s just a picture people need to understand the true nature of the zero-sum problem.

3) I basically agree, and I think the bigger problem with Sharpe is that people are guaranteed the market return only if they don’t trade. His mathematical proof that indexers always match the market is, of course, correct insofar as the passive investor who does nothing, gets the market return. But as soon as you trade, you’re an active investor in that period (Sharpe’s footnote 4). And the spread you have to pay to transact is the gain of the active player on the other side. So passive performance = active performance, but only because the passive investor has to briefly become an active investor in order to get fleeced. In order for the passive investor to match the market in practice, he must be able to trade in size at the market price and not allow himself be exploited. Which is not a bad assumption at small scale but gets harder as the passive investor gets bigger. (Sharpe hand-waves past this in footnote 3, saying trading makes the math more complicated but doesn’t change the basic principles. But if passive trading is big enough to move the market, if effective trading spreads are sufficiently large, that can no longer be true.)

Too much theories, no wonder investors’ need to hire advisors to help them out (I believe advisors give out lots of fake or wrong information). In addition, I believe investing is NOT a zero sum game and using a poker analogy is incorrect. Here are my thoughts:

Someone always win playing in the market and most people would pretty easily identify the individual. Many articles claim Mr.Buffett. Unfortunately, we never question what makes Mr. Buffett the winner in the first place. Mr. Buffett has a great average using cumulative return as a measurement. Look closely at the information you’ll find he doesn’t always beat the market. So what makes him a winner?

Poker analogy is incorrect because someone needs to be representing the house (which always win and I don’t believe is Mr. Buffett). I don’t play poker and don’t know the game too well. Please identified that player for me?

Finally, active investing will beat passive investing during a new bull market. This new bull market must include new tangible inventions (not financial innovation) that could help and improve society.

The question isn’t active vs passive. Price discovery is an essential function in capitalism, so we will always need active managers. The question is, how much active management do we need for effective price discovery? The truth is, the Grossman-Stiglitz paradox is irrelevant. Active managers don’t have to rely on arbitrage opportunities as compensation for their active efforts. If that were true, most would be out of business. Instead, they charge their fees whether they beat the market or not. They take advantage of the fact that everyone wants to beat the market, and they are really good at selling products claiming to do just that. The losers in the equation are the end investors. The winners are the asset gatherers charging high management fees for something they are unlikely to deliver.

The reality is the majority of people don’t have time (because of family/jobs/etcetera) or won’t put forth the necessary effort to study the market to become a good active investor.

Passive is necessary for the majority of individuals. Most active professionals can’t beat the market. Legendary investor Bill Miller beat the S&P 500 for 15 straight years. And then he ran flat for years and over his career cumulativly could NOT beat the market. Over a 25 – 30 year, active managers lose to the S&P 500 over 85% of the time.

The most important thing for most people:
Regular, monthly money into a passive fund while compounding for a long time will serve just fine.

The article all but ignored a very large category of active investors; namely the dumb ones who underperform on both time-weighted and money-weighted basis. They include 80% of the country’s active managers more or less.
I think the article would have sounded more realistic and maybe disheartening if it had focused on them instead of Mr. Buffett.
I had the honor of speaking to Mr. Buffett once by the way. He was slick and funny.

“Buffett also says most people should steer clear of active investing”

Buffett’s argument has always been that active management is overpriced, not that it is ineffective.

“Buffett, who makes a bid-ask market for the index, selling when it’s above his estimate of fair value and buying when it’s below fair value.”

Buffett cannot do this. He is the only active trader. There is no price but the price at which Buffett last traded. Consequently, the market is never mispriced unless Buffett makes it that way. how does “the market” become undervalued? the market is all active traders, you said so yourself.

More than 130 business leaders have responded to a deadlock in the UK Parliament by signing a letter calling for a second Brexit referendum to prevent a chaotic withdrawal from the EU. "The only feasible way to do this is by asking the people whether they still want to leave the EU," the letter says. CNBC (17 Jan.)

The Chinese government is likely to establish a growth target for this year that falls short of the 6.5% target set for 2018, sources said. This year's target is expected to be 6% to 6.5%. China Daily (Beijing) (18 Jan.)

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